Mathematics, 06.05.2020 06:08 quanyoung88

Suppose 6% of all people filing the long income tax form seek deductions that they know are illegal, and an additional 3% incorrectly list deductions because they are unfamiliar with income tax regulations. Of the 6% who are guilty of cheating, 76% will deny knowledge of the error if confronted by an investigator.
(a) If the filer of the long form is confronted with an unwarranted deduction and he or she denies the knowledge of the error, what is the probability that he or she is guilty?

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Answer from: uehlingt39

The probability that a person is guilty given that he or she denies the knowledge of the error is 0.6068.

Step-by-step explanation:

The Bayes' theorem states that the conditional probability of an event E $_{i}$ , belonging to the sample space S, given that another event A has already occurred is:

$P(E_{i}|A)=\frac{P(A|E_{i})P(E_{i})}{P(A|E_{1})P(E_{1})+P(A|E_{2}P(E_{2})+...+P(A|E_{n}P(E_{n})}$

Denote the events as follows:

X = illegal deduction is filed

Y = knowledge of the error is denied.

The information given is:

P (Cheating) = 0.06

P (Actual error) = 0.03

P (Y|X) = 0.76

Compute the probability of X as follows:

$P(X)=\frac{P(Cheating)}{P(Cheating)+P(Actual\ error)}=\frac{0.06}{0.06+0.03}=0.67$

The probability that a person who is not guilty will deny the knowledge of the error, is:

$P (Y|X^{c})=1$

Compute the value of P (X|Y) as follows:

$P(X|Y)=\frac{P(Y|X)P(X)}{P(Y|X)P(X)+P(Y|X^{c})P(X^{c})}$

$=\frac{0.76\times 0.67}{(0.76\times 0.67)+(1\times (1-0.67))}$

$=\frac{0.5092}{0.5092+0.33}$

=0.6068

Thus, the probability that a person is guilty given that he or she denies the knowledge of the error is 0.6068.

Answer from: Quest

x= 1

step-by-step explanation: convert 5\frac{11}{12}5

to improper fraction. use this rule: a \frac{b}{c}=\frac{ac+b}{c}a

ac+b

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{5\times 12+11}{12}3.25+0.5x+1

5×12+11

2 simplify 5\times 125×12 to 6060

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{60+11}{12}3.25+0.5x+1

60+11

3 simplify 60+1160+11 to 7171

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{71}{12}3.25+0.5x+1

4 simplify \frac{5}{6}x

x to \frac{5x}{6}

3.25+0.5x+1\frac{1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+1

5 convert 1\frac{1}{3}1

to improper fraction. use this rule: a \frac{b}{c}=\frac{ac+b}{c}a

ac+b

3.25+0.5x+\frac{1\times 3+1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

1×3+1

6 simplify 1\times 31×3 to 33

3.25+0.5x+\frac{3+1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

3+1

7 simplify 3+13+1 to 44

3.25+0.5x+\frac{4}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

8 simplify 3.25+0.5x+\frac{4}{3}+\frac{5x}{6}3.25+0.5x+

to \frac{13.75}{3}+\frac{4x}{3}

13.75

\frac{13.75}{3}+\frac{4x}{3}=\frac{71}{12}

13.75

9 simplify \frac{13.75}{3}

13.75

to 4.5833334.583333

4.583333+\frac{4x}{3}=\frac{71}{12}4.583333+

10 subtract 4.5833334.583333 from both sides

\frac{4x}{3}=\frac{71}{12}-4.583333

−4.583333

11 simplify \frac{71}{12}-4.583333

−4.583333 to \frac{4}{3}

\frac{4x}{3}=\frac{4}{3}

12 multiply both sides by 33

4x=\frac{4}{3}\times 34x=

×3

13 simplify \frac{4}{3}\times 3

×3 to \frac{12}{3}

4x=\frac{12}{3}4x=

14 simplify \frac{12}{3}

to 44

4x=44x=4

15 divide both sides by 44

x=1

Answer from: Quest

2/4 is the answer

step-by-step explanation:

x= total pieces

both ate 9 pieces

mindy ate 3 so troy ate 6

6= (1/4)x

x =24

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